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[Phys-L] Re: "moving clock runs slower" (yes)



On Tue, 13 Sep 2005, John Denker wrote (in pqrt):
____________________________snip_________________________________

Teaching in general and teaching relativity in particular consists
in large measure of providing a framework of ideas, notation, and
other formalism so that people can think about the topic without
risk of getting confused.

___________________________snip - snip____________________________________

I have presented the key ideas in analogical terms, i.e. comparing clocks
to odometers. I have given the graphical representation, i.e. spacetime
diagrams. I have also given the matrix representation. I have also
given the bivector / quaternion / Clifford algebra representation. If
this doesn't meet your standards, please tell me what *would* be good
enough for you.

___________________________snip-snip-snip_______________________________
For thousands of years, people have considered
the length of a ruler to be invariant with respect to rotations. The
projection of a ruler on the wall of the cave has been recognized as
not "really" a ruler, just a projection. As Joel R. says, it is "really"
a projection ... but it is not "really" a ruler.

It seems overwhelmingly probable that if people were more familiar with
rotations in the (t, x) plane -- i.e. boosts -- they would consider
the relevant property of a clock to be the invariant interval between
clock-ticks. Anybody in his right mind would want it this way, so why
not let it be this way?

To say the same thing in other words: considering just plain Euclidean
rotations, let the (x', y') frame be rotated relative to the (x, y) frame.
The tick-marks of either frame "(as viewed from the other frame)" will
appear foreshortened, but I haven't heard anybody arguing that either
frame "really" becomes shorter.
__________________________end snip_____________________________________
This, like many exchanges in this forum, is really about
communication. I'd like to interject my experience with all this, which
probably differs from that of many of you.
I was an aero-engineering undergrad, back when supersonic flight
was not yet discussed (I learned about it by reading captured German
documents shortly after I was first commissioned). I had no background in
relativity from college, that I can recall. My introduction was from a
fellow junior officer who'd had a good physics course at U Mich and who
taught me the "paradoxical" way that relativistic velocities add. So I
first had to get serious about relativity was in physics grad school.

Spacetime diagrams were a real hurdle. It may be true that you don't have
to be a rocket scientist to think of ct as a length - just like a space
dimension - but it wasn't that easy for me. Looking back, I'd say that
the big hurdle for me was the different signature of Minkowski space. It
is still a hurdle, although I hold my breath and analytically continue
from Minkowski to Euclidean and back again three times before breakfast
daily.

What I'm trying to say is that the analogy between spatial rotations and
boosts was striking when I became reasonably fluent in transformation
groups, it was not something that could have grabbed my attention earlier.
I would certainly not be so bold as to press that analogy upon high school
students. My preference would be to go at the topic like an
experimentalist. That's to say that the experimental physicist has to
confront SR on at least two occasions: (1) when measuring the lifetimes of
short-lived elementary particles and (2) when calculating the orbits of
charged particles moving in a magnetic field. Chemists, of course, have
tto deal with E=mc^{2}. Whether or not we want high school students to be
able to calculate with these ideas is a question I'll leave for another
discussion.
Regards,
Jack




--
"Trust me. I have a lot of experience at this."
General Custer's unremembered message to his men,
just before leading them into the Little Big Horn Valley
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